**Core Concept**
The patient's presentation of knee pain, irritability, gum bleeding, and characteristic radiographic findings of a thin cortex with a white line at the metaphysis is suggestive of a bone disorder affecting the metaphysis, a region of the bone where growth occurs. This condition is associated with defective bone formation and a propensity for fractures.

**Why the Correct Answer is Right**
The clinical presentation is consistent with **Caffey's disease**, also known as infantile cortical hyperostosis. This rare condition is characterized by inflammation of the periosteum, leading to excessive bone growth and cortical thickening in the affected area. The white line at the metaphysis, also known as the "corner sign," is a hallmark radiographic feature. Additionally, gum bleeding and irritability are common symptoms due to systemic inflammation.

**Why Each Wrong Option is Incorrect**
* **Option A:** Osteogenesis imperfecta is a genetic disorder leading to brittle bones, but it does not typically present with a white line at the metaphysis.
* **Option B:** Ewing's sarcoma is a malignant bone tumor, but it usually presents with a more aggressive clinical course, including pain, swelling, and systemic symptoms.
* **Option C:** Fibrous dysplasia is a benign bone disorder, but it typically affects the long bones and does not present with the characteristic white line at the metaphysis.

**Clinical Pearl / High-Yield Fact**
Caffey's disease is a rare condition, but it is essential to consider it in the differential diagnosis of children presenting with bone pain, irritability, and gum bleeding, particularly when radiographic findings of a white line at the metaphysis are present.

**Correct Answer:** C.